This result exactly confirms that both the critical exponents of \(\Delta r_{ph}/r_{phc}\)  and \(\Delta \mu _{ph}/\mu _{phc}\)  equal to \(1/2\)  at the critical point. That indicates from the viewpoint of thermodynamic black holes have more similar behaviors as the ordinary thermal systems, and they maybe also have the similar microstructures from the perspective of the statistics [1]}. Those conclusions strongly imply there exist a relationship between the photon sphere radius and phase transition of black holes.
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